Radiation in the terahertz portion of the electromagnetic spectrum can be generated using a variety of different techniques and physical mechanisms. One such technique for the production of terahertz waves involves nonlinear mixing of optical wave frequency components in an electro-optic material. For example, femtosecond optical pulse irradiation of electro-optic (EO) crystals such as lithium niobate (LN) and lithium tantalate (LT) can be used to generate terahertz phonon-polariton waves, hereafter referred to as “polaritons”, which include both electromagnetic and lattice vibrational components, and which propagate through the EO crystal at speeds that are a significant fraction (e.g., typically about 5-25%) of the speed of light in air (c). The polariton phase velocity inside the EO crystal is given by the ratio c/nTHz, where nTHz is the frequency-dependent EO crystal refractive index in the terahertz frequency range for the polariton polarization of interest. When a polariton wave encounters an edge of the EO crystal, it may be partially reflected and partially transmitted through the interface defined by the crystal edge. The medium on the other side of the crystal edge may be air, for example, and the process of polariton generation in an EO crystal may be used as a means for providing free-space terahertz radiation.
A primary mechanism for polariton generation in response to an ultrashort optical pulse is impulsive stimulated Raman scattering (ISRS). The ISRS process involves difference frequency mixing among optical frequency components within the bandwidth of the optical pulse in order to generate terahertz radiation at one or more frequencies that correspond to the optical frequency differences. The spatial and temporal properties of the generated polaritons can be controlled by suitably configuring the temporal and/or spatial profiles of the optical pulse used in the generation of the polaritons, see for example U.S. Pat. No. 6,075,640 entitled “SIGNAL PROCESSING BY OPTICALLY MANIPULATING POLARITONS” by K. A. Nelson, filed on Nov. 25, 1998, the contents of which are incorporated herein by reference. For example, if the optical pulse is focused cylindrically in an EO crystal, the generated polaritons may propagate substantially laterally relative to the direction of propagation of the optical pulse. FIG. 1 is a schematic diagram showing a plan view of polariton generation in an EO crystal in response to an incident optical pulse. Optical excitation pulse 100, propagating in the z-direction, is incident on EO crystal 102 and cylindrically focused therein. Polariton waves 104 and 106 are generated in response to pulse 100. Each polariton wave propagates substantially laterally (i.e., substantially in the x-direction) with a modest forward component in the z-direction. The forward propagation angle θ is about 25 degrees for ferroelectric EO crystals such as LN and LT, for example. The angle θ is given by the Cherenkov condition.
In general, the process of polariton generation as shown in FIG. 1 is not effectively phase-matched. That is, the terahertz field components of the polariton waves that are generated by the optical pulse as it moves from the front of the EO crystal to the back are not superposed constructively in order to produce a larger field amplitude than the field amplitude generated in any single region of the crystal. The EO crystal's terahertz-region refractive index, nTHz, is typically larger (e.g., from about nTHz=4 to about nTHZ=20) than the crystal's optical-region refractive index (e.g., about n=2), and so the optical pulse moves through the crystal at a faster speed than the terahertz polariton. As a result, the terahertz radiation propagates primarily laterally, rather than collinearly and phase-matched with the optical pulse, as would be the case if the refractive index values n and nTHz were equal. In some EO crystals such as ZnTe, the condition n=nTHz can be realized at particular optical and terahertz frequencies. However, in ferroelectric, high-dielectric crystals such as LN and LT, the above condition is generally not attained.
Although the disparity in optical and terahertz refractive indices typically prevents phase-matching in high-dielectric materials, the lateral propagation of the polariton response offers certain advantages. For example, the terahertz polariton field is conveniently accessible to additional optical pulses that can be used for probing the terahertz field characteristics, including real-space imaging of the terahertz field. Additional optical pulses can also be used in order to manipulate the terahertz polariton field as it propagates.
In addition, the EO crystal can be patterned with functional elements including terahertz waveguides, resonators, gratings, and other structures into which the polariton wave can be directed, enabling terahertz field guidance and control. Such structures are disclosed, for example, in “Terahertz polariton propagation in patterned materials,” Nature Materials 725: 95-98 (2002) by N. S. Stoyanov et al., the contents of which are incorporated herein by reference. Additional materials can be embedded within or placed adjacent to the EO crystal and/or its patterned features in order to create multifunctional hybrid structures that make use of the terahertz fields. These and similar capabilities, taken together, have been labeled “polaritonics” to suggest a broadly applicable platform for terahertz signal generation, control, guidance, use, and measurement. Without phase-matching, however, the efficiency of terahertz radiation generation is low. Therefore, a method for effective phase-matching of terahertz radiation generation in high-dielectric EO materials is of importance in practical terahertz signal processing applications, and also in scientific applications of terahertz radiation, including linear and nonlinear terahertz spectroscopy.